Incorporating the Effect of Coarse-Graining in the Compressible Pairwise Interaction Model

Compressible particle-laden flows occur in natural phenomena or engineering disciplines like atmospheric entry and supernova explosions. The Euler-Lagrange method is commonly used to simulate these systems, treating the fluid in an Eulerian frame while tracking particles individually in a Lagrangian framework. In such flows, particle forces vary significantly due to interactions with neighboring particles. Deterministic force models, such as compressible pairwise interaction models, which incorporate particle and neighbor locations, have been shown to accurately predict force variations in these complex systems.

For more realistic scale studies, however, due to the sheer number of particles involved, it is computationally costly to track each particle's motion. A solution to this is the employment of coarse-graining particles (also called particle parcels), where each parcel in the simulation accounts for the dynamics of a group of particles collectively in the real world. This study dives into the interplay of the pairwise interaction model and the coarse-graining method to reduce computational cost but maintain accuracy. We examine how the compressible Maxey-Riley-Gatignol equation, originally formulated for individual particles, adapts when applied to particle parcels—--where the surface-averaged operation in that equation must be corrected to account for the effects of coarse-graining. Comparisons between the model and particle-resolved simulation will be presented to investigate the validity of this coarse-grained compressible pairwise interaction model.